3 Answers
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I'll just take this out into an actual answer, and the answer is 'NO', the crop factor doesn't make it a 1.5:1 ratio. What it does change is the ratio of information per pixel which would be an valid new designation.

Why? Because the 1:1 ratio is a designation of how large the lens renders subjects on the focal plane whatever that plane is, it is an optical designation. A 2cm square subject will be rendered as 2cm squared on either a FF sensor or a 1.5x crop sensor. To suggest otherwise takes any meaning away from the designation since every body you put it on would effectively give it a different meaning. A 1:1 ratio is still a 1:1 ratio on a 10D at 6MP or a 5DmkII at 22MP or a 1.5x crop body at 18MP.

It'd be like saying with film, if a different film emulsion had better resolving power it'd changed the magnification power of the lens, or that printing it on a larger print did.

"A 2cm square subject will be rendered as 2cm square on either a FF sensor or a 1.5x crop sensor." I think that should be worded as "A 2cm square subject will be rendered as a 2cm square in the projected image circle." The projection is to an image circle, not to a specific sensor, and different sensor size will capture different amounts of that image circle. Because of APS-C's cropping, it is possible that you will not actually "record an image" of the full subject, as you would with a FF sensor. That was why I added the "sort-of" case in my answer.
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jrista♦Feb 18 '11 at 19:49

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I disagree, the properties of the 'sensor/film' don't matter and where a 2cm object falls on the sensor is besides the point. Mentioning that a 2cm subject may only be partially on the sensor/film belabors the point, so assuming the subject we're talking about is entirely on the sensor/film makes the answer more clear. Weather or not all of or part of a subject makes it onto the sensor/film has no impact on the ratio that it was recorded at and therefore is irrelevant.
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ShizamFeb 18 '11 at 20:18

I think your missing my point. It is only possible to achieve 1:1 magnification at the minimum focus distance. That means that you are projecting a specific image circle of a subject, and there are no alternative framing options to accommodate different sensor sizes. If you project a 2cm subject 2cm onto the image circle, the FF sensor is ultimately capturing less detail of the full subject, where as the APS-C is capturing more detail of part of the subject. If you reframe the FF to match the APS-C, you are no longer projecting a 1:1 image circle, since you are beyond the MFD of the lens.
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jrista♦Feb 20 '11 at 20:05

Yea, while we were discussing it yesterday in chat it came out that you were keeping FoV constant and I was not which led to some confusion. But again, since I'm interpreting the question from a purely optical standpoint ('allow the lens to magnify 1:1') FoV is irrelevant as is the pixel density of the sensor. So I think we're both right within the bounds of our own interpretation of the question.
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ShizamFeb 20 '11 at 20:16

I guess the answer is yes and no. Technically speaking, the image circle projected by the lens is 1:1, and your sensor is capturing a smaller part of the center of that circle...cropping it. This fits with the formula for magnification:

M = (di - f) / f

Where di is the distance from the lens to the sensor, and f is the focal length. Crop factor or sensor size is not taken into account when calculating the magnification of a lens. From this perspective, the purely optical perspective...the answer is no.

Now, when you factor megapixels and native print size into things, the answer is probably "sort of". If you have an APS-C and FF sensor with the same number of megapixels, the final unscaled "magnification" of the image in print would appear larger with the APS-C for two reasons. First, it packs more megapixels into less space, and second, that greater number of megapixels represents a smaller portion of the image (narrower field of view), which increases the apparent magnification. You could make a larger unscaled print of a smaller part of your subject with the APS-C than you could with the FF.

I thought the 1:1 designation was ment as a spec. for the representation of the object on the film/sensor only and has no bearing on display size. So the answer to this question would be 'NO', an object that is 2cm square would be projected onto either sensor at a max of 2cm square. no?
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ShizamFeb 18 '11 at 3:31

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@Shizam - You're correct, but so is Jon in a sense. The crop factor isn't so much important as the resolution of the sensor itself. A FF sensor with the same pixel density isn't going to provide less information than the APS-C in a unit of area, but one that has less density will. Having said that, there are other factors at play, such as diffraction limits, depth of field, etc. So, it's not cut and dry and you can't just apply the 1.5 multiplier to it in absence of that information.
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John Cavan♦Feb 18 '11 at 4:31

@Shizam: @John Cavan reiterated my point well. I was really just trying to say that it isn't as simple as a simple "NO", and at the same time, it isn't "YES" either. Its something in-between, and it depends on how you look at the subject. If you look at it from a purely optical perspective...then yes, you are correct. A 2cm square is projected 2cm in size on the image plane, regardless of how big the imaging medium is. However...thats just looking at it from the optical perspective.... ;)
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jrista♦Feb 18 '11 at 7:15

Ran outta characters to make a comment, must mean its more of an answer :)
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ShizamFeb 18 '11 at 16:14

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It might be useful to look at this as a case of digital magnification. Any sensor is sampling an image. The crop factor refers to how much of the image is sampled. The pixel sizes tell us the resolution of the sampling. Finer resolution is tantamount to magnification--up to a point. That point is determined by the quality of the optics and the f/stop.
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whuberFeb 18 '11 at 19:49

Okay, after talking with Shizam in the chat room, I think I'm going to take a stab at this questions.

Really, this is a question of semantics. The most commonly used definition of 1:1 means that the size of the object is the size of the image on the sensor. With a smaller sensor, the object will thus be smaller. But it's still a 1:1 really by the definition that I've applied. It will appear like a 1:1.6 image would if a full framed camera were to take the same image. If the pixel size on a full framed camera were the same, then the image would appear exactly the same. If the pixels were larger on the full framed (Most likely), then the image resolution will be slightly higher on the crop sensor, but still look the same as if it were cropped. Really what happens when you are using a crop sensor is that you are throwing away the outer edges of a full framed camera, but aside from that, everything else remains the same.

The minimum focal distance will remain exactly the same on the cropped sensor, BTW.